NDLI: Markov network processes with product form stationary distributions

Content Provider	Springer Nature Link
Author	Chao, X. Miyazawa, M. Serfozo, R.F. Takada, H.
Copyright Year	1998
Abstract	This study concerns the equilibrium behavior of a general class of Markov network processes that includes a variety of queueing networks and networks with interacting components or populations. The focus is on determining when these processes have product form stationary distributions. The approach is to relate the marginal distributions of the process to the stationary distributions of “node transition functions” that represent the nodes in isolation operating under certain fictitious environments. The main result gives necessary and sufficient conditions on the node transition functions for the network process to have a product form stationary distribution. This result yields a procedure for checking for a product form distribution and obtaining such a distribution when it exits. An important subclass of networks are those in which the node transition rates have Poisson arrival components. In this setting, we show that the network process has a product form distribution and is “biased locally balanced” if and only if the network is “quasi-reversible” and certain traffic equations are satisfied. Another subclass of networks are those with reversible routing. We weaken the known sufficient condition for such networks to be product form. We also discuss modeling issues related to queueing networks including time reversals and reversals of the roles of arrivals and departures. The study ends by describing how the results extend to networks with multi-class transitions.
Starting Page	377
Ending Page	401
Page Count	25
File Format	PDF
ISSN	02570130
Journal	Queueing Systems
Volume Number	28
Issue Number	4
e-ISSN	15729443
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer Communication Networks Systems Theory, Control Probability Theory and Stochastic Processes Operations Research/Decision Theory Production/Logistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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